{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Predicting Student Admissions\n",
    "\n",
    "In this notebook, we predict student admissions to graduate school at UCLA based on three pieces of data:\n",
    "- GRE Scores (Test)\n",
    "- GPA Scores (Grades)\n",
    "- Class rank (1-4)\n",
    "\n",
    "The dataset originally came from here: http://www.ats.ucla.edu/\n",
    "\n",
    "_Note: Thanks Adam Uccello, for helping us debug!_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## 1. Load and visualize the data\n",
    "\n",
    "To load the data, we will use a very useful data package called Pandas. You can read on Pandas documentation here:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 287,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>admit</th>\n",
       "      <th>gre</th>\n",
       "      <th>gpa</th>\n",
       "      <th>rank</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>380.0</td>\n",
       "      <td>3.61</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>660.0</td>\n",
       "      <td>3.67</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>800.0</td>\n",
       "      <td>4.00</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>640.0</td>\n",
       "      <td>3.19</td>\n",
       "      <td>4.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>520.0</td>\n",
       "      <td>2.93</td>\n",
       "      <td>4.0</td>\n",
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       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1</td>\n",
       "      <td>760.0</td>\n",
       "      <td>3.00</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1</td>\n",
       "      <td>560.0</td>\n",
       "      <td>2.98</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0</td>\n",
       "      <td>400.0</td>\n",
       "      <td>3.08</td>\n",
       "      <td>2.0</td>\n",
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       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1</td>\n",
       "      <td>540.0</td>\n",
       "      <td>3.39</td>\n",
       "      <td>3.0</td>\n",
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       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0</td>\n",
       "      <td>700.0</td>\n",
       "      <td>3.92</td>\n",
       "      <td>2.0</td>\n",
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       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0</td>\n",
       "      <td>800.0</td>\n",
       "      <td>4.00</td>\n",
       "      <td>4.0</td>\n",
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       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0</td>\n",
       "      <td>440.0</td>\n",
       "      <td>3.22</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>1</td>\n",
       "      <td>760.0</td>\n",
       "      <td>4.00</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>0</td>\n",
       "      <td>700.0</td>\n",
       "      <td>3.08</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>1</td>\n",
       "      <td>700.0</td>\n",
       "      <td>4.00</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>0</td>\n",
       "      <td>480.0</td>\n",
       "      <td>3.44</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>0</td>\n",
       "      <td>780.0</td>\n",
       "      <td>3.87</td>\n",
       "      <td>4.0</td>\n",
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       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>0</td>\n",
       "      <td>360.0</td>\n",
       "      <td>2.56</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>0</td>\n",
       "      <td>800.0</td>\n",
       "      <td>3.75</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>1</td>\n",
       "      <td>540.0</td>\n",
       "      <td>3.81</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>0</td>\n",
       "      <td>500.0</td>\n",
       "      <td>3.17</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>1</td>\n",
       "      <td>660.0</td>\n",
       "      <td>3.63</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>0</td>\n",
       "      <td>600.0</td>\n",
       "      <td>2.82</td>\n",
       "      <td>4.0</td>\n",
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       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>0</td>\n",
       "      <td>680.0</td>\n",
       "      <td>3.19</td>\n",
       "      <td>4.0</td>\n",
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       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>1</td>\n",
       "      <td>760.0</td>\n",
       "      <td>3.35</td>\n",
       "      <td>2.0</td>\n",
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       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>1</td>\n",
       "      <td>800.0</td>\n",
       "      <td>3.66</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>1</td>\n",
       "      <td>620.0</td>\n",
       "      <td>3.61</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>1</td>\n",
       "      <td>520.0</td>\n",
       "      <td>3.74</td>\n",
       "      <td>4.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>1</td>\n",
       "      <td>780.0</td>\n",
       "      <td>3.22</td>\n",
       "      <td>2.0</td>\n",
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       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>0</td>\n",
       "      <td>520.0</td>\n",
       "      <td>3.29</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>370</th>\n",
       "      <td>1</td>\n",
       "      <td>540.0</td>\n",
       "      <td>3.77</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>371</th>\n",
       "      <td>1</td>\n",
       "      <td>680.0</td>\n",
       "      <td>3.76</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>372</th>\n",
       "      <td>1</td>\n",
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       "      <td>2.42</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>373</th>\n",
       "      <td>1</td>\n",
       "      <td>620.0</td>\n",
       "      <td>3.37</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>374</th>\n",
       "      <td>0</td>\n",
       "      <td>560.0</td>\n",
       "      <td>3.78</td>\n",
       "      <td>2.0</td>\n",
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       "    <tr>\n",
       "      <th>375</th>\n",
       "      <td>0</td>\n",
       "      <td>560.0</td>\n",
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       "      <td>4.0</td>\n",
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       "    <tr>\n",
       "      <th>376</th>\n",
       "      <td>0</td>\n",
       "      <td>620.0</td>\n",
       "      <td>3.63</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>377</th>\n",
       "      <td>1</td>\n",
       "      <td>800.0</td>\n",
       "      <td>4.00</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>378</th>\n",
       "      <td>0</td>\n",
       "      <td>640.0</td>\n",
       "      <td>3.12</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>379</th>\n",
       "      <td>0</td>\n",
       "      <td>540.0</td>\n",
       "      <td>2.70</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>380</th>\n",
       "      <td>0</td>\n",
       "      <td>700.0</td>\n",
       "      <td>3.65</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>381</th>\n",
       "      <td>1</td>\n",
       "      <td>540.0</td>\n",
       "      <td>3.49</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>382</th>\n",
       "      <td>0</td>\n",
       "      <td>540.0</td>\n",
       "      <td>3.51</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>383</th>\n",
       "      <td>0</td>\n",
       "      <td>660.0</td>\n",
       "      <td>4.00</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>384</th>\n",
       "      <td>1</td>\n",
       "      <td>480.0</td>\n",
       "      <td>2.62</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>385</th>\n",
       "      <td>0</td>\n",
       "      <td>420.0</td>\n",
       "      <td>3.02</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>386</th>\n",
       "      <td>1</td>\n",
       "      <td>740.0</td>\n",
       "      <td>3.86</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>387</th>\n",
       "      <td>0</td>\n",
       "      <td>580.0</td>\n",
       "      <td>3.36</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>388</th>\n",
       "      <td>0</td>\n",
       "      <td>640.0</td>\n",
       "      <td>3.17</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>389</th>\n",
       "      <td>0</td>\n",
       "      <td>640.0</td>\n",
       "      <td>3.51</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>390</th>\n",
       "      <td>1</td>\n",
       "      <td>800.0</td>\n",
       "      <td>3.05</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>391</th>\n",
       "      <td>1</td>\n",
       "      <td>660.0</td>\n",
       "      <td>3.88</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>392</th>\n",
       "      <td>1</td>\n",
       "      <td>600.0</td>\n",
       "      <td>3.38</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>393</th>\n",
       "      <td>1</td>\n",
       "      <td>620.0</td>\n",
       "      <td>3.75</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>394</th>\n",
       "      <td>1</td>\n",
       "      <td>460.0</td>\n",
       "      <td>3.99</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>395</th>\n",
       "      <td>0</td>\n",
       "      <td>620.0</td>\n",
       "      <td>4.00</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>396</th>\n",
       "      <td>0</td>\n",
       "      <td>560.0</td>\n",
       "      <td>3.04</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>397</th>\n",
       "      <td>0</td>\n",
       "      <td>460.0</td>\n",
       "      <td>2.63</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>398</th>\n",
       "      <td>0</td>\n",
       "      <td>700.0</td>\n",
       "      <td>3.65</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>399</th>\n",
       "      <td>0</td>\n",
       "      <td>600.0</td>\n",
       "      <td>3.89</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>400 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     admit    gre   gpa  rank\n",
       "0        0  380.0  3.61   3.0\n",
       "1        1  660.0  3.67   3.0\n",
       "2        1  800.0  4.00   1.0\n",
       "3        1  640.0  3.19   4.0\n",
       "4        0  520.0  2.93   4.0\n",
       "5        1  760.0  3.00   2.0\n",
       "6        1  560.0  2.98   1.0\n",
       "7        0  400.0  3.08   2.0\n",
       "8        1  540.0  3.39   3.0\n",
       "9        0  700.0  3.92   2.0\n",
       "10       0  800.0  4.00   4.0\n",
       "11       0  440.0  3.22   1.0\n",
       "12       1  760.0  4.00   1.0\n",
       "13       0  700.0  3.08   2.0\n",
       "14       1  700.0  4.00   1.0\n",
       "15       0  480.0  3.44   3.0\n",
       "16       0  780.0  3.87   4.0\n",
       "17       0  360.0  2.56   3.0\n",
       "18       0  800.0  3.75   2.0\n",
       "19       1  540.0  3.81   1.0\n",
       "20       0  500.0  3.17   3.0\n",
       "21       1  660.0  3.63   2.0\n",
       "22       0  600.0  2.82   4.0\n",
       "23       0  680.0  3.19   4.0\n",
       "24       1  760.0  3.35   2.0\n",
       "25       1  800.0  3.66   1.0\n",
       "26       1  620.0  3.61   1.0\n",
       "27       1  520.0  3.74   4.0\n",
       "28       1  780.0  3.22   2.0\n",
       "29       0  520.0  3.29   1.0\n",
       "..     ...    ...   ...   ...\n",
       "370      1  540.0  3.77   2.0\n",
       "371      1  680.0  3.76   3.0\n",
       "372      1  680.0  2.42   1.0\n",
       "373      1  620.0  3.37   1.0\n",
       "374      0  560.0  3.78   2.0\n",
       "375      0  560.0  3.49   4.0\n",
       "376      0  620.0  3.63   2.0\n",
       "377      1  800.0  4.00   2.0\n",
       "378      0  640.0  3.12   3.0\n",
       "379      0  540.0  2.70   2.0\n",
       "380      0  700.0  3.65   2.0\n",
       "381      1  540.0  3.49   2.0\n",
       "382      0  540.0  3.51   2.0\n",
       "383      0  660.0  4.00   1.0\n",
       "384      1  480.0  2.62   2.0\n",
       "385      0  420.0  3.02   1.0\n",
       "386      1  740.0  3.86   2.0\n",
       "387      0  580.0  3.36   2.0\n",
       "388      0  640.0  3.17   2.0\n",
       "389      0  640.0  3.51   2.0\n",
       "390      1  800.0  3.05   2.0\n",
       "391      1  660.0  3.88   2.0\n",
       "392      1  600.0  3.38   3.0\n",
       "393      1  620.0  3.75   2.0\n",
       "394      1  460.0  3.99   3.0\n",
       "395      0  620.0  4.00   2.0\n",
       "396      0  560.0  3.04   3.0\n",
       "397      0  460.0  2.63   2.0\n",
       "398      0  700.0  3.65   2.0\n",
       "399      0  600.0  3.89   3.0\n",
       "\n",
       "[400 rows x 4 columns]"
      ]
     },
     "execution_count": 287,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "data = pd.read_csv('student_data.csv')\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Let's plot the data and see how it looks."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 288,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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6VkU3Y6xT1uE5g5ReHKzrramhgfpvfINN+fnUf+MbNDU0DJ1stcAFWA9Ln0ja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\niEgVBQwREamigCEiIlV+A+VAcccRlgOeAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1209cf160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "def plot_points(data):\n",
    "    X = np.array(data[[\"gre\",\"gpa\"]])\n",
    "    y = np.array(data[\"admit\"])\n",
    "    admitted = X[np.argwhere(y==1)]\n",
    "    rejected = X[np.argwhere(y==0)]\n",
    "    plt.scatter([s[0][0] for s in rejected], [s[0][1] for s in rejected], s = 25, color = 'red', edgecolor = 'k')\n",
    "    plt.scatter([s[0][0] for s in admitted], [s[0][1] for s in admitted], s = 25, color = 'cyan', edgecolor = 'k')\n",
    "    plt.xlabel('Test (GRE)')\n",
    "    plt.ylabel('Grades (GPA)')\n",
    "plot_points(data)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The data, based on only GRE and GPA scores, doesn't seem very separable. Maybe if we make a plot for each of the ranks, the boundaries will be more clear."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 289,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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6GTX6KKlmNr2mDwqNPMx0M3JHL7O5remDgnvl1pY7epnNbWVVNDeS2VY013KY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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1209cd550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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fMA4pnHjwINHZs5FbbiE6ezYnd3Vl3NbrSdgrrx3BXicbxuNxHhgR1NqLbGBA\nKRqr+eiQiCT0jYnsLsFJSWFM0QrbkMJ9+/bx8Vdf5T2vvsreL36RucC/A/v372fp0qVv2D7oPpR8\nhvh6aU6pr6/n6/Pnc97OnVT19dFVWck758/PGtTC1NxXqsaqKdwK/EBEGt2UF4tF5DZgE3BL4KUz\nJkBhG1IYj8d5MBajDliN04H3QCyWtTxBLlIzHkN8eydO5NCsWfz7LbdwaNYseidOzLit1+Ysk5+x\nUmc/ipPeIgL8hXubgLNYzqNBF86YIIUttXLQzUFhK8+2bdt49NAh+jo74QtfoK+zk0e7ujI2TxX7\nvIZiMWa+A1V9GWekkTElJWxDCsM2pHY8mqe8NN8V+4z1opFtEgPQAiwGKkZ57WycUWQfzWVChF83\nm7xmTGnwuh5Hua2v4Td8Soj3V8B7gJ+LyGMicp+I/FREngW+DuxW1f8XVMAyxpQur813YWteK1Wi\nWXKrDNtQZCZwBvAa8EtV7Q2uWJnNmzdPOzstmaox+Qjb6J10efbu3cvcHJqnvG4fNoX8+4vIblWd\nN+Z2uQaFsLCgYEx+RmYlbY9GqSqirKTFLj1ZsqOri57aWqLt7SSqqsYt3XyuQWGs5iNjTImw0TuF\nFcbJkqMJLCiISKWIPCoiT4jIkyKybpRtPi0iT4nIPhH5iYi8NajyGFMMglx0xutyrsZf2UZbhYnn\noCAip4rInBw2PQIsVNWLgLnAVe5M6KH24CzBOQfYAtzhtTzGjKcgT9pB52IqhfUmilnYJktmlMsQ\nJZz1k9+Ek9TwN0AH8KVc3uu+fyLwOJDIsk0c2DHWvmxIqimUoNeA9jpE06uBgQFtWLhQz66s1PeA\nnl1ZqQ0LF4Y2/3+pKfT6C/g0JDVtsqr+GfgvwHdUNQFcMdabRCQiInuBl4EHdEQOpRE+BozauCYi\nN4pIp4h0Hj58OMciG+OvoNvkx6N5wUtaCeOvsK1pnkmuQeEEETkDuA5ozXXnqppS1bnAdGC+iFww\n2nYicgMwD/hihv1sVNV5qjpv6tSpuX68GQfFvPC6V0G3yQfdvJDu6Oxbtw5iMfrWrRuzo7Ocvt/x\nEGSuKr/kGhSSQBvwa1V9TETOBn6V64eo6h+Bh4CrRr4mIlcA/wAsUdUjue7TFF65JSgLuk0+6FxM\nu3fvpqevD5qaoLcXmproOXKExx8ffQHFcvt+jSOnoKCqm1V1jqp+3H38rKp+INt7RGSqiJzi3j8Z\nuBL4+YgJquOJAAAXb0lEQVRt4jgzo5eok2PJ+CzIK71t27ZxcNcu1nR3M1GVNd3dvLBrV+iG2Pkl\n6Bm1+TQvePl+U6mUkyBi1y7YsMH599ixjMt92hDW8jRmQjwAEZkF/AswTVUvcEcfLVHV9VnedgZw\np4hEcILP3araKiJJnA6PrTjNRTFgs4gAPK+qS47jeMwQb5gs09hIYuNG39oxd+/eTV9PD01ALdAE\nHOnp4fHHHy/JBGXjkbDOy3oEXr/fSCQCS5YM67Ng6dKsy316TUDndcZu2GZYm9ybj/4VWIVTY0ZV\n9wHXZ3uDqu5T1bhbw7hAVZPu82vdgICqXqGq01R1rnuzgOCjoCfLpFIpFGeN3Q3uv8cg45Vnvp/h\npaYzXm3gGoJMAKN9v7uyfL81NTXEHnxweJ/FAw9QXV096vZem8u8Dqm15qlwyjUoTNQ3rp/g3y/f\nBCLo0SyRSIQlMOxKcilkvPL0yutJI+hx/mE7ie3evZvuK64Y/v1eeWXGPoLR+iwu8TEBndeLEGue\nCqdcg8IrInIOoAAicg3wYmClMr4IejRLTU0ND8Ziw64kH4hGM155euX1pJFPzchLzSJsJ7FUKsWE\n5uZh3++Ee+7JWFPz2mfhdc1lrxchNsM6nHINCjfhdAifJyJdwCeBjwdWKuOLoEezjHolecklvu3f\n60nD60nJ65V/2E5ikUiEsw4eJDZ7NnLLLcRmz+asrq6sNTWvQyK9bO/1ImTU5qmJE8M3w7fc5DLD\nLX0DosAkL+/x+2Yzmr0ZGBjQlpYWbWpq0paWFt9nTwa5f6+LqgS9aEvYFnlpaWnReDSq94A2gd4D\nOjcaLVh5vM7YPXLkiM449VQ9F/QW0HNBZ5x6qh45cmScS14eyHFGc9bU2SLy6TECypd8jVA5sNTZ\n5SN9JX+wo4O6nh7aolGmZ0n1PDga5+BBeurqiLa1kZg+PWMTSVNTE72NjWwY8htYJUI0mWT16tXH\nXZ6gha086TLlut5Ba2sra6+/nrU9PRwALgDWRaM0/eAHJTl6rdByTZ09Vo/gJPffc4GLga3u48XA\nyI5nY3zldQio1zWX4/E4jdEoye5uKnh9dE0yQ/NFua2hnG+Zch1Su2fPHup6e1kGLHOf6+jttTWX\nCyynRXZE5GfA1ar6qvt4EvBjVX1vwOV7A6speGPjwDML45V2OWltbaVxxQp2DQnKiViM5KZNvs2D\nMK/zdeU1EfkFMEfdNBQichKwT1XPPe6SemRBIXdhXGkrbD/qoJd3DOvxhqE8+TQPhu3/czHJNSjk\n2sH8D8ATwG3ubS/w2Vze6/fNOppzF7aO0aBTT4dNPseb7rhPJpO+d9yH8e/vZaBC2P4/Fxv8TJ2t\nqp8DPgr8wb39parenkewMuNoz549XNHdTRtOCoo24Mru7oINoQzbOP+geT3eoCfHhTFXlZchr2Eb\nEjweCpGlNueV11R1N7AJuAf4vYjMCKxUxhdz5szhzkiERqAXaATujES48MILC1KecvtRez3eoIPm\n0FxVvQzPVVUMym3luKBn6GeSU1AQkSUi8iucVde2u/+W5uVdiTmN4bmJTitgWcrtR+31eIMOmuOR\nqypIQWepDZugc5dlkmtNoQm4BPilqr4NZ9W1XYGVyvhi3759LDl2bNhJZsmxY+zfv78g5Sm3H7XX\n4w06aAadqypoXtNuFLvxWIlvVLl0POB2UOB0Nk9I38/lvX7frKM5d2HsmAt6hnXYeDne9BrKF1ZW\n6i2gF/q8hvKo/x8KOAPaZOf3mt34MaM5TUQexJlfsgGYgrPm8sWqemkwoSozG5KaOxuHX1xSqRTL\namt5eudOzuzr41BlJedfeinN7e2+fF/2/6G4eJ2hPxa/5ylEgddwmps+BEwGvq+qv8/ynkrgZ8BJ\nODOnt6hq44htTgK+A9QAvwc+qKrPZStL2INCmMaBDy1PUOPwjX/ymczllf1/8FfQv3c/vy/fgoK7\nctqDqvo+jwUQIKqq3SJSATwCfEJVdw3Z5m9xJsX9jYhcDyxX1Q9m22+Yg8IbVsJqbydRVeXbSmem\ntHnNxWQKq9h+77kGhTE7mlU1BRwTkcleCuA2Y3W7Dyvc28gItBS4072/BVjkBpOiVKjRAqY0lNvo\nrGJXqr/3XEcfdQP7ReSbIvLP6dtYbxKRiIjsxemDeEBVO0ZsUgW8AKCqA8CfgNNH2c+NItIpIp2H\nDx/Oscjjr2CjBUzeCjE5KJN8RmeFqfzlplR/77kGhR8Ba3D6CHYPuWWlqilVnQtMB+aLyAX5FFJV\nN6rqPFWdN3Xq1Hx2MS6CXunM+Ctsy2t6HXJZqMlNpcxLkC3Z33suQ5T8uAFrgc+MeK4NeJd7/wTg\nFdx+jky3MA9J9brIiCmsMA7Z9cLvIYvlbvD3W13t/H6rq7P+fovt944fuY9EZKmI3DTkcYeIPOve\nrhnjvVNF5BT3/snAlcDPR2y2FfiIe/8a4Kdu4YuS1zVwTWEVe9qNUm2+KBSvfQSl+nsfq/noFl5f\nWAec4aUXA5cz9hrNZwAPicg+4DGcPoVWEUmKyBJ3m28Cp4vIM8CngZUeyx86XtfANYUzHh27Qbb5\nl2zzRYHkE2RL8veerRoBPDbi8VeH3N+VS1XE71uYm49McUmnko67qaTjPqeSDjpV9Xg0XwSZyjts\n5Sn15jh8WqP5GVV9e4bXfq2q5/gfprIL8zwFU3yCnMw1HiuLBVn+sI3DD3qRHb9nEIeNL4vsAN8H\n/mqU5/8a2JRL1PH7ZjUFUyySyaSuFFF1O7IVdKWINjU1jbp92BbBCduV83gMDCjl3Fz4tMjOp4C/\nFJGHROR/ubeHgb8APpl/zDKm9HntswjbIkRh68gej4EBJdlH4FHWoKCqL6uT9K4JeM69JVX1Xar6\nu+CLZ0zx8joZLWyjocLWkW0zvsdHTgnxwsT6FEwx8dLmPx4J8bwIWxt7OWZ59TPhnq9ZUsPEgoIp\nVWE86YUtq2rYyhMkvzvWcw0KxbHkkjFlIJ3mIn3SS4bgpJduYy9ETSWbYruYzcfQPqYKINndTcLt\nYwry+7CgYEyIhPUkHAYjr5wbo1E2lnDzUbY+piD/f+SaEM8YYwoqbKOzglaojnULCsaYohC20VlB\nyyeVuh+s+ciYMhK25WK9iMfjNEajJIeMzmqLRkmW6JDUQvUxldXoo2L+QRhzvIJOExG0MI7OKiY2\nJHWEsOVxMWa8hW0eRD7KaUiq33xbo7lUlOp6qsbkqhTa5C0NRfDKJiiELY+LMePN0kSYXJRNUAhb\nHhdjxluhRrOY4hJYn4KInAV8B5gGKLBRVb8yYpvJwPeAGTgjof5RVb+Vbb/H3acQkjwuxhSCtcmX\nr4J3NIvIGcAZqvq4iEwCdgPLVPWpIdt8FpisqreKyFTgF8BbVLU/0379GH1kPwhjcmMj9kpHwXMf\nqeqLwIvu/VdF5GmgCnhq6GbAJBERIAb8JzAQVJkshYAxuSu3tBJhVIigPC6T10RkJhAHOka89FVg\nK3AImAR8UFWPjfL+G4EbAWbMmBFkUY0xrkIlZDOOQgXlwDuaRSQG/BD4pKr+ecTLdcBe4ExgLvBV\nEXnTyH2o6kZVnaeq86ZOnRp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      "text/plain": [
       "<matplotlib.figure.Figure at 0x120927a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ico6q7hlje+8BFgNvGWc7W3CuVFi8eHG0+tCaiuH113pubx1qaxlIp+lNJied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\nxhiTZUHBGGNMlgUFY4wxWf8HxDVUF3MUO0oAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12094add8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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uwbhEKibr1XAa6lvSYqaEsaB4wd3/umhRk09IJmS9THY2Q32Pjo6yceNGVq5c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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1209beeb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data_rank1 = data[data[\"rank\"]==1]\n",
    "data_rank2 = data[data[\"rank\"]==2]\n",
    "data_rank3 = data[data[\"rank\"]==3]\n",
    "data_rank4 = data[data[\"rank\"]==4]\n",
    "plot_points(data_rank1)\n",
    "plt.title(\"Rank 1\")\n",
    "plt.show()\n",
    "plot_points(data_rank2)\n",
    "plt.title(\"Rank 2\")\n",
    "plt.show()\n",
    "plot_points(data_rank3)\n",
    "plt.title(\"Rank 3\")\n",
    "plt.show()\n",
    "plot_points(data_rank4)\n",
    "plt.title(\"Rank 4\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "These plots look a bit more linearly separable, although not completely. But it seems that using a multi-layer perceptron with the rank, gre, and gpa as inputs, may give us a decent solution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# 2. Process the data\n",
    "We'll do the following steps to clean up the data for training:\n",
    "- One-hot encode the rank\n",
    "- Normalize the gre and the gpa scores, so they'll be in the interval (0,1)\n",
    "- Split the data into the input X, and the labels y."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 301,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import keras\n",
    "from keras.utils import np_utils\n",
    "\n",
    "# remove NaNs\n",
    "data = data.fillna(0)\n",
    "\n",
    "# One-hot encoding the rank\n",
    "processed_data = pd.get_dummies(data, columns=['rank'])\n",
    "\n",
    "# Normalizing the gre and the gpa scores to be in the interval (0,1)\n",
    "processed_data[\"gre\"] = processed_data[\"gre\"]/800\n",
    "processed_data[\"gpa\"] = processed_data[\"gpa\"]/4\n",
    "\n",
    "# Splitting the data input into X, and the labels y \n",
    "X = np.array(processed_data)[:,1:]\n",
    "X = X.astype('float32')\n",
    "y = keras.utils.to_categorical(data[\"admit\"],2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 302,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of X: (400, 7)\n",
      "\n",
      "Shape of y: (400, 2)\n",
      "\n",
      "First 10 rows of X\n",
      "[[ 0.47499999  0.90249997  0.          0.          0.          1.          0.        ]\n",
      " [ 0.82499999  0.91750002  0.          0.          0.          1.          0.        ]\n",
      " [ 1.          1.          0.          1.          0.          0.          0.        ]\n",
      " [ 0.80000001  0.79750001  0.          0.          0.          0.          1.        ]\n",
      " [ 0.64999998  0.73250002  0.          0.          0.          0.          1.        ]\n",
      " [ 0.94999999  0.75        0.          0.          1.          0.          0.        ]\n",
      " [ 0.69999999  0.745       0.          1.          0.          0.          0.        ]\n",
      " [ 0.5         0.76999998  0.          0.          1.          0.          0.        ]\n",
      " [ 0.67500001  0.84750003  0.          0.          0.          1.          0.        ]\n",
      " [ 0.875       0.98000002  0.          0.          1.          0.          0.        ]]\n",
      "\n",
      "First 10 rows of y\n",
      "[[ 1.  0.]\n",
      " [ 0.  1.]\n",
      " [ 0.  1.]\n",
      " [ 0.  1.]\n",
      " [ 1.  0.]\n",
      " [ 0.  1.]\n",
      " [ 0.  1.]\n",
      " [ 1.  0.]\n",
      " [ 0.  1.]\n",
      " [ 1.  0.]]\n"
     ]
    }
   ],
   "source": [
    "# Checking that the input and output look correct\n",
    "print(\"Shape of X:\", X.shape)\n",
    "print(\"\\nShape of y:\", y.shape)\n",
    "print(\"\\nFirst 10 rows of X\")\n",
    "print(X[:10])\n",
    "print(\"\\nFirst 10 rows of y\")\n",
    "print(y[:10])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# 3. Split the data into training and testing sets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 292,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x_train shape: (350, 7)\n",
      "350 train samples\n",
      "50 test samples\n"
     ]
    }
   ],
   "source": [
    "# break training set into training and validation sets\n",
    "(X_train, X_test) = X[50:], X[:50]\n",
    "(y_train, y_test) = y[50:], y[:50]\n",
    "\n",
    "# print shape of training set\n",
    "print('x_train shape:', X_train.shape)\n",
    "\n",
    "# print number of training, validation, and test images\n",
    "print(X_train.shape[0], 'train samples')\n",
    "print(X_test.shape[0], 'test samples')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# 4. Define the model architecture"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 309,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "dense_75 (Dense)             (None, 128)               1024      \n",
      "_________________________________________________________________\n",
      "dropout_21 (Dropout)         (None, 128)               0         \n",
      "_________________________________________________________________\n",
      "dense_76 (Dense)             (None, 64)                8256      \n",
      "_________________________________________________________________\n",
      "dropout_22 (Dropout)         (None, 64)                0         \n",
      "_________________________________________________________________\n",
      "dense_77 (Dense)             (None, 2)                 130       \n",
      "=================================================================\n",
      "Total params: 9,410.0\n",
      "Trainable params: 9,410.0\n",
      "Non-trainable params: 0.0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "# Imports\n",
    "import numpy as np\n",
    "from keras.models import Sequential\n",
    "from keras.layers.core import Dense, Dropout, Activation\n",
    "from keras.optimizers import SGD\n",
    "from keras.utils import np_utils\n",
    "\n",
    "# Building the model\n",
    "# Note that filling out the empty rank as \"0\", gave us an extra column, for \"Rank 0\" students.\n",
    "# Thus, our input dimension is 7 instead of 6.\n",
    "model = Sequential()\n",
    "model.add(Dense(128, activation='relu', input_shape=(7,)))\n",
    "model.add(Dropout(.2))\n",
    "model.add(Dense(64, activation='relu'))\n",
    "model.add(Dropout(.1))\n",
    "model.add(Dense(2, activation='softmax'))\n",
    "\n",
    "# Compiling the model\n",
    "model.compile(loss = 'categorical_crossentropy', optimizer='adam', metrics=['accuracy'])\n",
    "model.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# 5. Train the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 310,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<keras.callbacks.History at 0x124708128>"
      ]
     },
     "execution_count": 310,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Training the model\n",
    "model.fit(X_train, y_train, epochs=200, batch_size=100, verbose=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# 6. Score the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 308,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " 32/350 [=>............................] - ETA: 2s\n",
      " Training Accuracy: 0.719999999659\n",
      "32/50 [==================>...........] - ETA: 0s\n",
      " Testing Accuracy: 0.679999997616\n"
     ]
    }
   ],
   "source": [
    "# Evaluating the model on the training and testing set\n",
    "score = model.evaluate(X_train, y_train)\n",
    "print(\"\\n Training Accuracy:\", score[1])\n",
    "score = model.evaluate(X_test, y_test)\n",
    "print(\"\\n Testing Accuracy:\", score[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# 7. Play with parameters!\n",
    "You can see that we made several decisions in our training. For instance, the number of layers, the sizes of the layers, the number of epochs, etc.\n",
    "\n",
    "It's your turn to play with parameters! Can you improve the accuracy? The following are other suggestions for these parameters. We'll learn the definitions later in the class:\n",
    "- Activation function: relu and sigmoid\n",
    "- Loss function: categorical_crossentropy, mean_squared_error\n",
    "- Optimizer: rmsprop, adam, ada"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": []
  }
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